"Nuisance parameters, composite likelihoods and a panel of GARCH models"
Cavit Pakel
Department of Economics, University of Oxford & Oxford-Man Institute, University of Oxford,
Eagle House, Walton Well Road, Oxford OX2 6ED, UK.
Neil Shephard
Oxford-Man Institute, University of Oxford, Eagle House, Walton Well Road, Oxford OX2 6EE, UK
and Department of Economics, University of Oxford
Kevin Sheppard
Oxford-Man Institute, University of Oxford, Eagle House, Walton Well Road, Oxford OX2 6ED, UK
& Department of Economics, University of Oxford
Abstract
We investigate the properties of the composite likelihood (CL) method for (T ×N_T ) GARCH
panels. The defining feature of a GARCH panel with time series length T is that, while nuisance
parameters are allowed to vary across N_T series, other parameters of interest are assumed to
be common. CL pools information across the panel instead of using information available in a
single series only. Simulations and empirical analysis illustrate that in reasonably large T CL
performs well. However, due to the estimation error introduced through nuisance parameter
estimation, CL is subject to the “incidental parameter” problem for small T .
Keywords: ARCH models; composite likelihood; nuisance parameters; panel data
JEL Classifications: C01, C14, C32